Given that u=3w^(4)-5, find (d)/(dw)(4w^(2)-sin u) in terms of only w. Answer:

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Given that  u=3w^(4)-5, find  (d)/(dw)(4w^(2)-sin u) in terms of only  w. Answer:

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Identify Function and Rule: We need to find the derivative of the function 4w^2 - sin(u) with respect to w. To do this, we will use the chain rule, which states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is 4w^2 - sin(x) and the inner function is u = 3w^4 - 5.Differentiate Outer Function: First, we differentiate the outer function with respect to u, treating w as a constant. The derivative of 4w^2 with respect to u is 0, since w is treated as a constant and the derivative of -sin(u) with respect to u is -cos(u).Differentiate Inner Function: Next, we differentiate the inner function u = 3w^4 - 5 with respect to w. The derivative of 3w^4 with respect to w is 12w^3, and the derivative of -5 with respect to w is 0. So, the derivative of u with respect to w is 12w^3.Apply Chain Rule: Now, we apply the chain rule by multiplying the derivative of the outer function with respect to u by the derivative of the inner function with respect to w. This gives us (0 - cos(u)) * 12w^3.Simplify Expression: Simplify the expression by distributing the 12w^3 across the terms inside the parentheses. This results in -12w^3 * cos(u).Express Derivative in Terms of w: Finally, we need to express the derivative in terms of w only. Since u = 3w^4 - 5, we substitute u back into the expression -12w^3 * cos(u) to get -12w^3 * cos(3w^4 - 5).

Given that $u=3 w^{4}-5$ , find $\frac{d}{d w}\left(4 w^{2}-\sin u\right)$ in terms of only $w$ . $\newline$ Answer:

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Given that u=3w4−5 u=3 w^{4}-5 u=3w4−5, find ddw(4w2−sin⁡u) \frac{d}{d w}\left(4 w^{2}-\sin u\right) dwd​(4w2−sinu) in terms of only w w w.\newlineAnswer:

Given that $u=3 w^{4}-5$ , find $\frac{d}{d w}\left(4 w^{2}-\sin u\right)$ in terms of only $w$ . $\newline$ Answer: